Multimodal two-echelon city logistics under space and time limitations

Abstract

This study explores how integrating inland waterways into multimodal distribution systems can enhance city logistics, alleviate street-level congestion, and ultimately improve the livability of the urban environment. To capture the operational complexities of such systems under severe space scarcity and regulatory access constraints, we formulate a multi-trip two-echelon vehicle routing problem. The model explicitly accounts for the physical limitations of dense city centers by incorporating storage-free satellites and spatial constraints for vehicle occupancy. While the first requires precise spatiotemporal synchronization between interacting vehicles during the transshipment operation from one mode to the other, the latter bounds the maximum number of transshipments occurring at the same time at a satellite. To evaluate system performance under these conditions, we develop an optimization framework driven by an iterative decomposition-based heuristic. The approach integrates a capacitated assignment model with routing heuristics through an adaptive workload-bounding feedback loop, ensuring that downstream routing constraints actively shape upstream customer-to-satellite assignments to find a feasible solution that attains the target service level while heuristically minimizing resource consumption. The methodology is demonstrated through a large-scale case study of a multimodal distribution system in Amsterdam, serving over 750 HoReCa businesses. To derive strategic insights from this operational model, we conduct a comprehensive scenario analysis of 10560 instances. The proposed framework identifies the minimum operational resources required to guarantee service coverage by systematically evaluating diverse strategic decisions in terms of network design, transshipment modalities, workforce levels, and city access time windows. The results illustrate practical trade-offs for urban logistics planning: relaxing full-coverage service targets (e.g., to 90%) provides substantial infrastructure savings, while denser satellite networks reduce street-level travel distances and increase zero-emission walking deliveries. Furthermore, enabling parallel transshipments with an adaptive workforce allows a significantly smaller network to maintain full service coverage.